Two prong racks work well for a traditional shape/size of bike but don't work so well in your situation.The way you have to use the two pronged rack means the bike is positioned off centre and tends to over hang the side of the car.
I've found fitting two bikes of differing sizes can be a problem too.
We have a single prong Ezi Grip rack which uses clamps to hold the bike. The prong in in the centre of the car and you can position the bike so that the bike is centrally located across the rear of the car.
The clamps can be rotated on the prong to best match the angle of the cross bar on the bike and can be adjusted along the prong to allow proper spacing between the bikes.
Have a look at the MC series here to see what I mean. http://www.ezigrip.co.nz/wp-content/uploads/2013/11/EZI-Modular-V5.pdf
I know this isn't the type of rack you have bought and I don't know if they do a version that will fit without having to have a tow bar. However you may find this style of rack may be better suited to your situation.